Gamnitude, Saphe, and Other Terms From Cepstral Litftering

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Gamnitude, Saphe, and Other Terms From Cepstral Litftering

You are probably aware that speech and image processing use spectral (frequency) analysis. You may not be aware that it is the spectrum of the spectrum that is used for the feature sets. By rearranging the letters in spectrum we get: Cepstrum. Many other useful (and amusing) terms are coined!

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An earlier post defined cepstrum and quefrency. This post explains some of the other quirky terms introduced in the same paper by Bogert, Healy, and Tukey. (Given Tukey’s delight in coining words, we can assume he was the member of the trio responsible for the new terms.)

The paper [1] explains why the new twists on familiar words:

In general, we find ourselves operating on the frequency side in ways customary on the time side and vice versa. Experience has made it clear that “words that sound like other words,” although strange at first sight, considerably reduce confusion on balance. These parallel or “paraphrased” words are made by the interchange of consonants or consonant groups, as in “
alanysis” from “analysis,” and are introduced as needed.

The magnitude and phase of a cepstrum are called gamnitude and saphe. (The latter explains the pun “saphe cracking” in the title.)

Filtering in the cepstral domain is called liftering. A high-pass filter corresponds to a long-pass lifter and a low-pass filter corresponds to a short-pass lifter.

Harmonics in spectra correspond to rahmonics in cepstra.

Some of these terms are helpful. As explained in the previous post, the independent variable in cepstral analysis, quefrency, differs enough from frequency that it helps to have a separate term for it. Using the terms long and short rather than high and low is helpful for the same reason. Using repiod for the analog of period seems gratuitous, but maybe it’s necessary for consistency. Once you introduce some new terminology, you have to keep going.

[1] Bruce P. Bogert, M. J. R. Healy, John W. Tukey. The Quefrency Analysis of Time Series for Echoes: Cepstrum, Pseudo-Autocovariance, Cross-Cepstrum and Saphe Cracking. Collected works of John Tukey volume 1